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ABCD is a rectangle with points E and F lying on sides AB and CD respectively. If the area of quadrilateral AEFD equals the area of quadrilateral CBEF, then which of the following statements is necessarily false with respect to the rectangle ABCD?
(2014)
  • a)
    Length of AE is always equal to the length of CF.
  • b)
    If the length of BC is 4 units, then the smallest integral length of EF is 5 units.
  • c)
    Length of AE is equal to the length of DF.
  • d)
    ∠AEF = ∠EFC
Correct answer is option 'B'. Can you explain this answer?
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ABCD is a rectangle with points E and F lying on sides AB and CD respe...
Option (a) – The length of AE is always equal to the length of CF because E and F is midpoint of side AB and CD.
So, statement – I is always true.
Option (b) : the Length of BC is equal to length of EF so statement II is always False.
Option (c) : Length of AE is equal to the length of DF because of EF is parallel to BC
Option (d) : ∠AEF = ∠EFC = 90°
So statement III is also true.
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Most Upvoted Answer
ABCD is a rectangle with points E and F lying on sides AB and CD respe...
Since AEFD and CBEF have the same area, we know that the base multiplied by the height is the same for both quadrilaterals. Let's call the length of AE x and the length of CF y.

a) Length of AE is always equal to the length of CF.
This statement is true because x and y are equal since the base multiplied by the height is the same for both quadrilaterals.

b) If the length of BC is 4 units, then the smallest integral length of EF is 5 units.
This statement could be true or false. Since we don't have any information about the length of BC, we can't determine the length of EF. So, this statement is not necessarily false.

c) Length of AE is equal to the length of DF.
This statement is true because both AE and DF are the same base of the rectangle ABCD.

d) The length of BC is equal to the length of AF.
This statement is necessarily false. Since the length of BC is the height of the rectangle and AF is one of the sides of the rectangle, they can't be equal.

Therefore, the necessarily false statement is d) The length of BC is equal to the length of AF.
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ABCD is a rectangle with points E and F lying on sides AB and CD respectively. If the area of quadrilateral AEFD equals the area of quadrilateral CBEF, then which of the following statements is necessarily false with respect to the rectangle ABCD?(2014)a)Length of AE is always equal to the length of CF.b)If the length of BC is 4 units, then the smallest integral length of EF is 5 units.c)Length of AE is equal to the length of DF.d)∠AEF = ∠EFCCorrect answer is option 'B'. Can you explain this answer?
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ABCD is a rectangle with points E and F lying on sides AB and CD respectively. If the area of quadrilateral AEFD equals the area of quadrilateral CBEF, then which of the following statements is necessarily false with respect to the rectangle ABCD?(2014)a)Length of AE is always equal to the length of CF.b)If the length of BC is 4 units, then the smallest integral length of EF is 5 units.c)Length of AE is equal to the length of DF.d)∠AEF = ∠EFCCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about ABCD is a rectangle with points E and F lying on sides AB and CD respectively. If the area of quadrilateral AEFD equals the area of quadrilateral CBEF, then which of the following statements is necessarily false with respect to the rectangle ABCD?(2014)a)Length of AE is always equal to the length of CF.b)If the length of BC is 4 units, then the smallest integral length of EF is 5 units.c)Length of AE is equal to the length of DF.d)∠AEF = ∠EFCCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABCD is a rectangle with points E and F lying on sides AB and CD respectively. If the area of quadrilateral AEFD equals the area of quadrilateral CBEF, then which of the following statements is necessarily false with respect to the rectangle ABCD?(2014)a)Length of AE is always equal to the length of CF.b)If the length of BC is 4 units, then the smallest integral length of EF is 5 units.c)Length of AE is equal to the length of DF.d)∠AEF = ∠EFCCorrect answer is option 'B'. Can you explain this answer?.
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